1. The nonlinear dynamics of SIS100 at injection G. Franchetti Beam dynamics meet Magnets II 18/4/2012G.Franchetti1 Magnet multipoles: Dipole: Akishin et al., V. Kapin, S. Sorge Quadrupole: Akishin et al. Resonance compensation: S. Aumon, F. Kesting, H. Liebermann, C. Omet, D. Ondreka, R. Singh

2. GSI and upcoming FAIR facility 18/4/2012G.Franchetti2 pbar-target/separator

3. SIS100 injection plateau scenario 10/05/2011G. Franchetti MAC 53 Nominal N ions = 6.25 x 10 10 /bunch Beam1:  x/y = 35/15 mm-mrad (2  )  Q x/y = -0.21/-033 Turns = 1.57 x 10 5 (1 sec.) First bunch @ 200 MeV/u Problem of control of beam loss for the bunched beams in SIS100 during 1 second sec 1 5 x 10 11 U 28+ SIS18 200 MeV/u 1000 MeV/u 18 Tm SIS100 50 Tm 11.4 MeV/u

4. Accelerators at the high intensity frontier 18/4/2012G.Franchetti4 QQ 0 -0.5 turns 0 10 2 10 3 10 4 10 5 SIS18 SIS100 SNS AGS Booster AGS MR JPARC UMER PSB JPARC RCS Challenge Short term storage Long term storage Higher Intensity 10 6 10 7 LHC ? Collider Higher Energy PS SPS

5. 18/4/2012G.Franchetti5 Nonlinear Resonances single particle motion (incoherent) orbit deformations long term effects: resonances and dynamic aperture High Intensity effects many particle force (coherent) short term effects coherent beam motion strong in linac High intensity + Nonlinear errors + Long storage Source of the effects: Magnets nonlinear components Source of effects: direct and indirect coulomb forces (i.e. the beam itself)

6. 18/4/2012G.Franchetti6 Machine resonances, dynamic aperture, and space charge

7. Interplay of resonances and space charge 17/11/2014G. Franchetti7 Periodic crossing of a resonance z x Bare tune Lattice error or Space Charge Structure Resonance Slow halo formation If halo is too large slow beam loss take place Pipe z Modeling of space charge induced resonance loss G. Franchetti and I. Hofmann Proc. of 20th ICFA Advanced Beam Dynamics Workshop: High Intensity High Brightness Hadron Beams (AIP, New York, 2002), 642, 260. Interplay of DA and space charge not studied

8. all normal and skew components in all dipoles and quadrupoles including also the gradient components (up to order 15) where skew missing the random component is taken as for the normal component (ansatz). the random component is taken arbitrarily to 30% of the systematic one. Residual closed orbit deformation: +/- 2 mm (conservative) 18/4/2012G.Franchetti8 Working example

9. Possible resonances: among 30 seeds 18/4/2012G.Franchetti9

10. Example with the seed #13 normal sex skew sex normal quad skew quad skew sex normal quad 18/4/2012G.Franchetti10

11. seed #13 For a test  coasting beam of 50x20 + δp/p = 5x10 -4 Much smaller beam loss for 35x15 coasting beam 18/4/2012G.Franchetti11

12. For a bunched beam 35x15 + δp/p=5x10 -4, no space charge Some small beam loss due to chromaticity 18/4/2012G.Franchetti12

13. (seed #13) INCLUDING SPACE CHARGE 18/4/2012G.Franchetti13 First bunch Large beam loss are not acceptable Also problems of self-consistency in beam tracking 10 – 15% beam loss do not affect code prediction

14. The situation of seed #13 + space charge 18/4/2012G.Franchetti14 first bunch

15. Compensating the half integer, coupling, norm + skew much better 18/4/2012G.Franchetti15 first bunch

16. Compensating also of the 3 rd order, normal and skew 18/4/2012G.Franchetti16 first bunch

17. Over the full cycle before acceleration ramp 10 % beam loss compensating simultaneously 6 resonances is not a bad result! But skew corrector should be active as well. Remark: Resonances should be corrected without violating the perturbative character of the theory. Here for 3 rd order it is not good. Certainly the magnet sorting will help to contain the driving terms of the uncorrected machine The effect of the self-consistency is the next step, and the assessment of the dynamics during acceleration 18/4/2012G.Franchetti17

18. Beam loss is difficult to predict 18/4/2012G.Franchetti18 In the CERN-PS experiment, code prediction of beam loss was 50% less than what measured. In the S317 code prediction of beam loss was 50% less than what measured. Beam loss depends on all details of the machine, and it is very difficult to predict them.

19. Resonance compensation Issues 18/4/2012G.Franchetti19 It is not known how resonance compensation will work with a high intensity beam, in a regime of periodic resonance crossing Experimental verification on SIS18 as a test example. This is the counter part of the ongoing activity at CERN

20. Experimental program 17/11/2014G. Franchetti20 1)Overview of the resonance situation in the SIS18 2)Study of the resonance Qx + 2 Qy = 11 through the beam loss 3)Attempt of compensation with sextupoles 4)Long term beam survival in a moderate high intensity without correction 5)Long term beam survival in a moderate high intensity with correction

21. Resonance chart of SIS18 @ 16/7/2014 17/11/2014G. Franchetti21

22. Tune ramp 17/11/2014G. Franchetti22 1 second Acceleration QyQy Tune ramp Q x = 4.2 kept always constant QyQy QxQx Beam always coasting Intensity low

23. Beam 17/11/2014G. Franchetti23 Injection has been set to fill machine acceptance – beam coasting

24. The resonance Q x + 2Q y = 11 17/11/2014G. Franchetti24 Stop-band

25. Modifying the resonance 17/11/2014G. Franchetti25 Resonance characterized by resonance driving term We try to assess the slowest oscillating resonance driving term K 2j are the normal integrated sextupolar strength of all errors and correctors

26. Situation according to theory 17/11/2014G. Franchetti26 ΛcΛc ΛsΛs all nonlinear objects that excite the Qx + 2 Qy = 11 UNKNOWN Excited by controlled sextupoles KNOWN Λ Θ Effective resonance strength ΛeΛe ΘeΘe

27. Resonance crossing and beam loss 17/11/2014G. Franchetti27 Effective driving term The pair allows the determination of

28. Attempt of correction with small Λ 17/11/2014G. Franchetti28

29. Best correction achieved 17/11/2014G. Franchetti29

30. 30 (δx) max ~ 6 mm small compared with the filled acceptance Bunched beam stored for 1 second 17/11/2014G. Franchetti Without resonance correction Bunched -> harmonics 4 before bunching SIS18 acceptances: 200x50 mm-mrad No significant effect of chromaticity and dispersion Experimental data

31. 17/11/2014G. Franchetti31 Without resonance correction With resonance correction Experimental data

32. Effectiveness of the compensation 17/11/2014G. Franchetti32 Experimental data

33. Conclusion / Outlook 17/11/2014G. Franchetti33 0) Periodic resonance crossing induced by space charge is a damaging mechanism, producing beam loss 0.1) Beam loss are very difficult to be predicted reliably… 1) Dynamics of particles near the coupled 3 rd order resonance is very challenging. fix point  fix lines. 2) Interplay of fix lines with space charge difficult to study especially in relation with periodic crossing. 3) Resonance control is a mitigation strategy, but its effectiveness with space charge is not part of the established “know how”. 3) Experimental campaign @ GSI proved that resonance compensation may work under space charge condition and periodic resonance crossing. 1)Complete the tests in a controlled environment and compare with simulations 2)Random magnet errors have big impact when coupled with space charge.

34. 18/4/2012G.Franchetti34 Design/ Construction Measurements = knowing real devices (with limits) Theory Magnet Beam Dynamics performance correction selection ? Beam based investigation of the machine last chance highly painful and long, involve : BD, Control, BI Beam Dynamics Beam Instrum. Machine control group …..